Surfaces carved out of patterned solid material are unlike folded developable surfaces in that the texture pattern on a carved solid varies on the surface as a function of the shape. Thus, unlike for developable surfaces, 3D shape extraction cannot be based on the assumption that textural changes in retinal images occur solely due to the projection. We first compared the perception of sinusoidally corrugated developable and carved surfaces, and then examined carved doubly-curved sinusoidal depth plaids that are inherently non-developable. We assumed the 2D patterns in parallel planes of the pre-carved solid to be identical. In all comparisons, the planar pattern of the carved surface matched the pattern on the developable surface. Veridical 3D shape perception of developable surfaces requires orientation modulations of critical components (Zaidi & Li, 2002). In perspective images of carved surfaces, similar critical orientation modulations arise from the same texture components, but spatial frequency modulations are greatly reduced. Frequency modulations in images of developable surfaces arise from changes in surface depth and slant, but for carved surfaces they arise almost entirely from changes in depth. As a result, concavities and convexities of isotropically textured developable surfaces are often perceptually confused due to similar slant-caused frequency modulations, but these confusions do not occur for carved surfaces. Perceived depth modulations along carved surfaces were much less and more gradual than along physically identical developable surfaces. Veridical perception of concavities, convexities, and saddles of depth plaids also require the visibility of critical orientation modulations about each of the two axes of depth modulation. However, isolated doubly-curved concavities often appear convex or flat. Despite differences in surface texture mapping between developable and carved surfaces, 3D shape percepts rely on similar orientation modulations.